def factorial_iter(n):
    '''Returns the factorial of n using iteration.'''
    answer = 1
    for i in range(1, n + 1):
        answer *= i
    return answer


def factorial(n):
    '''Returns the factorial of n using recursion.'''
    print('computing {0}!'.format(n))
    if n == 0:
        print('I know the factorial of 0!')
        return 1
    else:
        answer = factorial(n - 1) * n
        print('computed {0}! = {1}'.format(n, answer))
        return answer


def strlen_iter(some_string):
    '''Return the length of some_string without using len.'''
    count = 0
    for next_char in some_string:
        count += 1
    return count


def strlen(some_string):
    '''Recursively return the length of some_string.'''
    print('I want the length of {0}'.format(some_string))
    if some_string == '':
        # base case: no recursive call
        print('the empty string has length 0')
        return 0
    else:
        # recursive case
        answer = 1 + strlen(some_string[1:])
        print('the length of {0} is {1}'.format(some_string, answer))
        return answer
        

def num_digits(num):
    '''Return the number of digits in (non-negative) num.'''
    print('I want the number of digits in {0}'.format(num))
    if num < 10:
        print('base case: num digits of {0} is 1'.format(num))
        # base case
        return 1
    else:
        # recursive case
        answer = 1 + num_digits(num / 10)
        print('recursive: num digits of {0} is {1}'.format(num, answer))
        return answer


def power(base, n):
    '''Return base raised to the power n.'''
    if n == 0:
        return 1
    else:
        return base * power(base, n - 1)